Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x-y &= 1 \\ 3x-6y &= 3\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-6y = -3x+3$ Divide both sides by $-6$ to isolate $y$ $y = {\dfrac{1}{2}x - \dfrac{1}{2}}$ Substitute this expression for $y$ in the first equation. $-2x-({\dfrac{1}{2}x - \dfrac{1}{2}}) = 1$ $-2x - \dfrac{1}{2}x + \dfrac{1}{2} = 1$ Simplify by combining terms, then solve for $x$ $-\dfrac{5}{2}x + \dfrac{1}{2} = 1$ $-\dfrac{5}{2}x = \dfrac{1}{2}$ $x = -\dfrac{1}{5}$ Substitute $-\dfrac{1}{5}$ for $x$ back into the top equation. $-2( -\dfrac{1}{5})-y = 1$ $\dfrac{2}{5}-y = 1$ $-y = \dfrac{3}{5}$ $y = -\dfrac{3}{5}$ The solution is $\enspace x = -\dfrac{1}{5}, \enspace y = -\dfrac{3}{5}$.